GM sure knows how to take care of their customers.
You might consider the generator. Since the '87 model year, they have an extremely high failure rate due to the huge voltage spikes they develop. Those spikes destroy the internal diodes and voltage regulator, and they interfere with computer sensor signals. While computers are very sensitive to low and fluctuating voltage, none are more intolerant than GM's digital dashes. In fact, on most of their vehicles with them, they switch from monitoring system voltage right at the generator to monitoring it right at the instrument cluster; it's that critical, at least in preventing annoying flickering display brightness.
I would start by having the generator load-tested with a professional tester, on the engine; don't take it off and haul it to an auto parts store. Professional load testers measure output capacity and "ripple". A bad diode will reduce the maximum output current to exactly one third of its designed output current, and ripple will be very high. Ripple is usually not displayed as a voltage. It is shown on a relative bar graph from low to high.
If you do find the generator is causing the problem, to prevent repeat failures, replace the perfectly good battery at the same time unless it is less than about two years old. As they age, they lose their ability to dampen and absorb those harmful voltage spikes.
Another way to identify if the generator is the cause of the problem is to start with a fully charged battery, then unplug the small connector on the rear, side of the generator, then see if the dash is working properly. If it is, suspect the generator. The dash should also work properly with the ignition switch turned on but without starting the engine.
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Friday, June 1st, 2012 AT 8:56 PM